Fiber for distortion-free propagation

ABSTRACT

A fiber for use in the propagation of light pulses with the attendant elimination of distortion. The fiber is useful as a delay line storage device for computer information with an extremely high-packing density capability for the bits of information. Another application is in a broadband communication system as a transmission line and in any application the fiber may be &#39;&#39;&#39;&#39;active&#39;&#39;&#39;&#39; as either a laser amplifier or oscillator. Basically, the invention involves the choice of fiber core and cladding size and other parameters to counteract, with the anomalous dispersion associated with the waveguide transmission, the normal dispersion of the bulk glass from which the fiber is made. The pulses of light are thereby propagated undistorted since the various frequency components within the light pulse are propagated with an effective velocity which is independent of wavelength in the spectral interval of the pulse.

United States Patent Snltzer 51 Feb. 29, 1972 FIBER FOR DISTORTION'FREEPrimary Examiner-Rodney D. Bennett, .Ir. PROPAGATION AssistantExaminer-N. Moskowitz Attorney-William C. Neaion, Noble S. Williams,Robert J. [72] Inventor. Elias Snitzer, Wellesley, Mass. Bird andBernard L Sweeney [73] Assignee: American Optical Corporation, M A

Southbridge, Mass.

[22] Filed: Nov. 14, 1969 [57] ABSTRACT [21] Appl. No.: 876,838 A fiberfor use in the propagation of light pulses with the attendantelimination of distortion. The fiber is useful as a delay line storagedevice for computer information with an extreme- PI. 1 {if} Kim..mmlffiaii lfifi 1y Making dew capability for we W 581 mm of Search.331/945; 33014.3; 350/96 P' F- f" is T"" as a transmission line and inany application the fiber may be active as either a laser amplifier oroscillator. Basically, the [56] Rem-em cued invention involves thechoice of fiber core and cladding size UNITED STATES PATENTS and otherparameters to counteract, with the anomalous dispersion associated withthe waveguide transmission, the 3,109,065 10/1963 McNaney ..350/96normal dispersion f the l glass f m hi h th fiber is 3,308,394 3/1967 Pmade. The pulses of light are thereby propagated undistorted 3,508,1654/1970 Nicolai ..350/96 Since the various frequency components withinthe light pulse OTHER PUBLICATIONS c. G. Young, Gliss Lasers, 7/69, pg.1267- 1289. Uchida, IEEE, 7.7, A Light Focusing Fiber Guide, May 26, 69.

. -C- H9155. Hi h. Csbsisseefl lka System at 1.062lu, lEEE10.5; wIEEE'ZLZ l-iolstjfitection With a Fiber Laser Preamplifier at 1.06u, May26, 69.

are propagated with an effective velocity which is independent ofwavelength in the spectral interval of the pulse.

DETECTOR PATENIEIIFEBZS I972 3. 646,462

SHEET 1 OF 2 -|O I2 LIGHT PULSE PULSE V I F/ G. GENERATOR I MODULATORLIGHT I6 PULSES ELECTRICAL SIGNAL ELECTRICAL FOR CONTROL SIGNAL TO OTHERCIRCUITRY V I I8 LIGHT PULSE DETECTOR HE ow c 2| TM Q ,j T55 Q 0 A HEIICUT-OFF 20 qg o? IIJVI'JNIYJH. ELIAS SNITZER w wm FIBERFORDISTORTION-FREE PROPAGATION This invention relates primarily to fiberoptic devices and more particularly to the construction of such devicesfor use as a propagation medium for a high density of information withsubstantially distortion-free output.

With the advent of mode-locked pulses whose duration is of the order ofseconds, a number of devices can be considered to utilize such pulses.For instance,:a delay line storage device, for computer information canadvantageously use a high density storage medium to propagate lightpulses generated :by one or more mode-locked oscillators and associatedcircuitry. The light from the pulse generator is modulated in oneof anumber of ways, such as allowing or not allowing the given pulse topass, or some other scheme for indicatingtwoormore states for theinformation contained in a single pulse or a group of pulses. The pulsesof light may then be focusedby a lens into a long fiber (of the order ofseveral inches and evenmeters inlength). The output of the fiber canthe'nbe received by a detector whose output is used both to control themodulator for recirculation of the light pulses through the fiber andalso as the input forother circuitry. By way-of preliminary explanation,it should be understood that the phrase mode-locked pulses refers topulses wherein the phase relationship between various frequencies issuch that there is coherent reinforcement at one time and one positionin the propagation anddestruction at other positions at the same time inthat medium.

In these and other schemes, it may be seen that very short pulses aredesired for high storage density capability. It is now possible toproduce very short pulses in the picosecond domain. As an example, apulse of 10 seconds has a spatial extent in'glassofapproximately-two-tenths of a millimeter. A 2-meter-long fiber couldthen in principle store 10 bits of information. If "the fibers arepacked with a density of 10 microns .center-to-center spacing, al-centimeter squared crossfzsection would contain 10 fibers. Suchapropagation medium wouldathen provide an information density capabilityof 10" bits=with an access timedetennined by the propagation time forlight in the 2-meter-long fiber, which would be 10 seconds.

Inorder to. utilize-the inherent high density. of storage provided bypicosecond pulses, it is necessary that the pulsesnot experience adistortion intheir shape, and, in particular, the distortion should notbe of .the type that would elongate the pulse. Asthe pulses get shorter,the special content of the pulses gets larger according to the followingrelationship:

where 1' is the pulse duration and All is the bandwidth of the pulse.

Therefore, a pulse duration of 10 seconds produces approximately a301Angstrombandwidth. According to normal dispersion,-the higherfrequencies in the bandwidth created propagate at slower velocities,this normal dispersion-being due to-the-glass material chosen for thecoreand cladding of the fiber.

Accordingly, a primary object of the present invention is to provide afiber optics construction to obtainessentiallysinglemode transmission ofa pulse of light having a band of frequency components. The fiber devicehas the property that the waveguide mode characteristics ofthe fiberproduce effective anomalous dispersionwhich cancels the normaldispersion of the bulk glass of which the fiber is made to avoidpropagation distortion. A more particular object is to provide a groupvelocity for propagation of the mode which has anegative dispersivevalue, that is, the group velocity has a higher value at higherfrequencies than the group velocity at lower frequencies in the pulse.

Anotherwapplication for propagation of light in fibers withoutdispersive distortion is .as a transmission line in a broadband:communications system; here the information would be an .amplitude orfrequency modulated carrier frequency or could be in the form of pulsecode modulation.

Theseand other objects are accomplished in one illustrative embodimentof the present invention wherein fiber size and other parameters thereofare chosen toallow substantially single-mode propagation. By 'chosing asmall enough fiber-core or a low enough frequency of propagation,single-mode propagation can be obtained. Howevenbecause of therelationship between frequency and the 'propagationconstant for lowfrequencies in particular, it may be shown that the group velocity ofmode propagation decreaseswithhigher frequencies below the cutoff pointfor certain higher ordermodes. It is therefore desirable to operateabove thecutoff point in the relationship between frequencyand thepropagation constant. It is known that higher order modes are potentialsources of additional pulse distortion by crosstalk of informationbetween propagating modes. It is, therefore, necessary to not onlyobtain a high enough change in group velocity of mode propagation perchange in frequency tobe above some higher order mode cutoff point, butalso to provide an absorbing cladding to eliminate the more off-axishigher order modes.

The above brief description, as well as further objects, features andadvantages of the present invention will-bemore fully appreciated byreference to the following detailed description of a presentlypreferred, but nonetheless illustrative embodiment in accordance withthe present invention, when taken in conjunction with the accompanyingdrawing, wherein:

FIG. 1 is a schematic block diagram of a system in which the presentinvention is useful;

FIG. 2 is a graphical representation of the relationship betweenfrequency and the propagation constant for group and phase velocity incertain of the lower order modes;

FIG. 3 is a sectional representation along the line 3-3 of FIG. 1 of afiber constructed according to: thepresent invention; and

FIG. 4 is a graphical representation of'the relationship between thefiber characteristic of fractional change in group index of refractionper fractional change in the-waveguide of propagation versus thewaveguide mode parameter for various indices of refraction of the corematerial.

Referring particularly to the drawings, FIG. I represents a system usinga fiber constructed according to the present invention as a delay linestorage device for computer information. A string of pulses is generatedby light pulse generator 10, which is made up of one or more mode-lockedoscillators together with associated circuitry (not shown). With veryshort pulses in the picosecond domain beingproduced, a pulse of loseconds has a spatial extent in the 2-meter fiber bundle 16 oftwo-tenths of a millimeter. The fiber 16 stores, therefore, 10 bits ofinformation. If the fiber bundle 16 is'constructed from a number offiber optic devices whose center-tocenter packing densityis 10 microns,a l-centimeter squared cross section of the fiber bundle 16 contains lofibers. An information density capability of l0 bits is then attainedwith an access timed determined by the propagation time for light in the2-meter-long fiber which would be 10 second. Each fiber in the bundlewould have its own'pulse modulator and pulse detector.

0! course, other applications are possible for utilization of the shortduration pulses. An exarnpleis a pulsed-code-modulationcommunicationsystem. Hereysingle-mode fibers would be "used 1 as thetransmission line for sending information between transmitter andreceiver. Just as in the delay line storage shown in FIG. 1', it isnecessary for maximum utiliza;

tion of the system (maximum data rate for the communication system aswell as maximum storageper unit length of delay line storage element)that the pulses of light which'represent the information be as short aspossible and that no distortion, and, in particular, elongation 'of thepulses take place.

Referring specifically to FIG. 2, mode lines are shown'as curves forproviding the relationship between the'propagation constant h for thegiven waveguide mode and the circular frequency to. It is 'customary'todraw the mode linewith the vertical coordinate w and the horizontalcoordinatehplt should be understood that a waveguide mode .ischaracterized by a dependence on time t and z, a direction parallel tothe waveguide axis such that the various electric and magnetic fieldcomponents all have z and t dependencies given by the followingtrigonometric equation:

exp [Kill-mil] where w=21rc/)\, the frequency of the light transmitted.Also, the propagation constant I: is a function of the frequency w, theradius a of the core of the fiber, the indices of refraction n, and m ofthe core and cladding, respectively, and the particular mode which isbeing considered. The various mode lines of FIG. 2 are represented bycurves which are confined to the region, as shown in FIG. 2, bounded bythe two straight lines through the origin whose slopes are c/n, and clnThe lowest order I-IE, mode propagates at all frequencies, but all othermodes have cutoffs, that is, for a given mode, propagation is notpossible at frequencies below the cutoff frequency. The cutoff frequencyfor the nearly degenerate group of modes that are able to propagatebeyond the HE mode is at a frequency (0 represented by line 20, which isthe lowest frequency at which that goup of modes can propagate in thefiber. The nearly degenerate set of three modes, HE TM and TE is shownwith only one mode line to describe them. From the mode line, the groupvelocity and the phase velocity are graphically described in FIG. 2. Ina case where the frequency of propagation is such that the propagationoccurs in the HE mode at any point on the graph of FIG. 2, the slope ofthe line connecting that point to the origin of the graph is the phasevelocity V and the slope of the tangent to the mode line at this pointis the group velocity V Assuming n is the index of refraction of thefiber cladding and n is the index of refraction of the core, the HE modeis characterized by the fact that it asymptomically approaches the linewith slope 0/11, as the frequency reduces to zero. It asymptomaticallyapproaches the line with slope cln, as the frequency is allowed toincrease to very larger values. This produces a curve whose slope as afunction of frequency first decreases as the frequency is increased fromzero. passes through an inflection point at which (dV /dw is zero, andthen the slope as a function of frequency increases to the final valuec/n, for very high frequencies. For clarity in this discussion, theinflection point hereafter will be referred to as point A in FIG. 2.Since we want higher frequencies to have greater group velocities, andbelow point A the group velocity decreases with higher frequency,whereas above point A the group velocity increases with higherfrequencies. the desired range of the curve is above the point A.

As stated previously, however, operation above point A is also above thecutoff frequency for the next higher order modes, so that propagation ofthe higher order modes TE TM and HE is also enabled. In order to deterthe effect of these higher order modes and still operate above point A,other means are available such as the use of an absorbing cladding.Operation of a clad fiber at frequencies above the inflection point forV as a function of frequency is a necessary condition for the fiber togive an anomalous dispersion that cancels the normal dispersion of theglass, but is not a sufficient condition for this desired result. Inaddition, the difference in indices of refraction between core andcladding must be sufficiently great to give a large enough anomalousdispersion to cancel the glass dispersion, since for larger indexdifferences the rate of change of V with w is greater than for smallindex differences. For example, for a cladding glass of n =l .8, m-n,should be 0.1 or greater.

A convenient description of the propagating modes in a circular fibercan be expressed in terms of a parameter u which is defined by thefollowing equation:

For a less than 2.405. only the HE mode propagates. For a value of ubetween 2.405 and 3.832, the higher order modes TE TM,,,, and HE, canalso propagate, and the still higher order modes are cut off. Thisrange, therefore, is the desired operating range for the parameter u inthe graph of FIG. 4.

in order to determine the required radius for the core of the clad fiberit is necessary to calculate the values of the propagation constant h asa function of the frequency w. This calculation requires the solution ofa transcendental equation which depends on Bessel and Hankel functions.The equation to be solved is given in the published article entitledCylindrical Dielectric Waveguide Modes" by E. Snitzer, Journal of theOptical Society of America Vol. 51, No. 5, pp. 491-498 (May 1961). Therequired equation for solution is eq. 20 of the above article. Thesolution provides the mode line as shown in FIG. 2. After obtaining thedata for the mode line, the slope of the mode line can be calculated asa function of frequency or of the core radius. This latter calculationhas been carried out and is given in FIG. 4. For convenience, the datais presented for [A(c/V,,- ,,,)()\/A)\)] as a function of the parameter:4 which was previously defined. The data in FIG. 4 is presented on theassumption that the cladding has an index of refraction n 1.50, but withthree different curves for values of the core index equal to 1.53,1.6824, and 1.72.

Summarizing briefly, in order to obtain substantially singlemodepropagation without pulse distortion, the fiber core 22 (FIG. 3) must beof a size to support not only the lowest order HE mode, but also thenext higher order group of modes. In order to both satisfy therequirement of no pulse distortion by effective zero net dispersion andavoidance of the complexities of multimode propagation, absorption inthe cladding can be utilized to selectively attenuate the higher ordermodes. Therefore, fibers should be used which satisfy the zerodispersion requirement (operation above point A on FIG. 2) but in whichthere is added to the cladding 24 constituents absorbing to the lightpropagated in the core 22. Since the higher order modes are moreoff-axis and propagate with greater light intensity in the cladding 24than the lowest order mode, the absorbing constituent in the claddingattenuates the higher order modes more severely. 1f laser light ispropagated in the core 22 at 1.06 microns, a cladding glass whichcomprises suitable concentrations of Sm can be used. At 1.06 micronsother ions which are suitable for absorbing capability in the claddingare Dy, Fe and Cu. The samarium is preferable for use with neodymiumglass fiber lasers.

Rather than uniformly dispersing the samarium through the cladding, itis also possible, as shown in FIG. 3, to clad the core 22 with a thinclear glass cladding 24 and then to utilize a second glass cladding 26,having an index of refraction n:, which includes the samarium. Forappropriately thin first claddings 24 (approximately one-tenth toone-fourth the value of A), there is enough penetration to attenuate thehigher order modes, but at the same time provide much less attenuationto the HE mode. The following table represents some of the actual fiberconstructions which were operated as lasers according to the presentinvention without distortion:

. n. n, n:

By use of the glasses of FIGS. 2 and 4 and in accordance with the abovedescription, the following example is presented for the design of afiber device in order to provide a more complete understanding of thepresent invention:

Assume that the core glass for the fiber device is a neodymium dopedlead flint silicate glass having an index of refraction of 1.6824 at1.060 microns wavelength and an index of refraction of 1.6833 at 1.014microns wavelength, and the cladding glass is a samarium-doped alkali,alkaline earth silicate glass having an index of refraction of 1.4986 at1.060 microns wavelength and an index of refraction of 1.4992 at 1.014microns wavelength. The measured normal dispersion would ruin): nan-r beapproximately 2 .0 3Xl0* and t l 1 e a ip malous dispersion.

a .85 microns radius of core The cladding n if a double-clad fiber shownin FIG. 3 were used with cladding n clear and cladding n samarium doped,would be chosen to be approximately l/l0-l/4 of the wavelength (1.060microns) in thickness.

While mode-locked pulses can be obtained in laser oscillators in which asaturable dye is included to give mode-locked, Q-switched output, it iswell known that the pulses so generated at the present time are erraticin shape. A further use of the present invention is to use an activefiber, constructed as described herein, as an amplifier for shaping anerratically generated mode-locked, Q-switched pulse from an appropriateoscillator into a well-shaped pulse whose half-intensity is l0 secondsor less by producing a saturated steady-state pulse in the amplifier.

I claim:

1. A fiber optic device for use as a light transmission line including acore and cladding, said core having an index of refraction, m, inrelation to the index of refraction, 11 of the cladding at thewavelength of transmission, A, and a radius, a,

which provides a dispersion in the group velocity for propagation in agiven dielectric waveguide mode which is equal in magnitude and oppositein sign to the nonnal dispersion of the material of which said core ismade, said indices of refraction, said radius and said wavelength oftransmission being related by the following expression A V m "4'' whereu is greater than approximately 2.6.

2. The invention according to claim 1 wherein said given mode is thelowest order HE mode.

3. The invention according to claim 2 wherein said cladding includes aconstituent absorbing to the light of the transmitted wavelength so thatthe higher order modes are absorbed more than said HE mode.

4. The invention according to claim 3 wherein said core includes alaserable material.

5. The invention according to claim 3 wherein said wavelength oftransmission is 1.06 microns and said cladding is a samarium-dopedglass.

6. The invention according to claim 5 wherein said core includes aneodyminum-doped glass.

7. The invention according to claim 3 wherein said wavelength oftransmission is 1.06 microns and said cladding is a glass doped with anelement chosen from a group consisting of Sm, Dy, Fe Cu.

8. The invention according to claim 1 wherein said core includes alaserable material and said fiber optic device is used as atravelling-wave amplifier for shaping a generated light pulse incidentto said device.

9. The invention according to claim 1 wherein said transmission line isa delay line storage device for a computer.

10. The invention according to claim 1 wherein said transmission line isfor use in a broadband communication system.

1. A fiber optic device for use as a light transmission line including acore and cladding, said core having an index of refraction, n1, inrelation to the index of refraction, n2, of the cladding at thewavelength of transmission, lambda , and a radius, a, which provides adispersion in the group velocity for propagation in a given dielectricwaveguide mode which is equal in magnitude and opposite in sign to thenormal dispersion of the material of which said core is made, saidindices of refraction, said radius and said wavelength of transmissionbeing related by the following expression
 2. The invention according toclaim 1 wherein said given mode is the lowest order HE11 mode.
 3. Theinvention according to claim 2 wherein said cladding includes aconstituent absorbing to the light of the transmitted wavelength so thatthe higher order modes are absorbed more than said HE11 mode.
 4. Theinvention according to claim 3 wherein said core includes a laserablematerial.
 5. The invention according to claim 3 wherein said wavelengthof transmission is 1.06 microns and said cladding is a samarium-dopedglass.
 6. The invention according to claim 5 wherein said core includesa neodyminum-doped glass.
 7. The invention according to claim 3 whereinsaid wavelength of transmission is 1.06 microns and said cladding is aglass doped with an element chosen from a group consisting of Sm3 , Dy3, Fe2 Cu2 .
 8. The invention according to claim 1 wherein said coreincludes a laserable material and said fiber optic device is used as atravelling-wave amplifier for shaping a generated light pulse incidentto said device.
 9. The invention according to claim 1 wherein saidtransmission line is a delay line storage device for a computer.
 10. Theinvention according to claim 1 wherein said transmission line is for usein a broadband communication system.